A light emitting element drive circuit and a display system able to simultaneously perform constant current control and PWM control and able to perform a stable adjustment of luminance over a wide dynamic range, including a constant voltage source having an output voltage adjustment unit able to be changed in output voltage according to a signal from the outside, a switch circuit connected to the cathode side of the LED and ON/OFF controlled in accordance with a PWM signal from the outside, a current detection unit for detecting the current flowing in the circuit, and a sample and hold circuit for maintaining the current input value from the current detection unit for a constant period, and the output voltage adjustment unit receives as input the output of the sample and hold circuit, that is, the current value when the switch circuit is ON, and adjusts the output of the constant voltage source so that this value becomes a previously determined set value, to thereby make the current flowing in the LED constant.